ChiGaM卫星静态重力场模型构建与分析

doi:10.11947/j.AGCS.2025.20250189

测绘学报 ›› 2025, Vol. 54 ›› Issue (10): 1798-1811.doi: 10.11947/j.AGCS.2025.20250189

ChiGaM卫星静态重力场模型构建与分析

谭勖立¹(), 李姗姗¹(), 黄志勇², 潘宗鹏²^,³, 范雕¹, 万宏发¹, 裴宪勇¹, 徐振邦¹

^1.信息工程大学地理空间信息学院，河南　郑州　450001
^2.智能空间信息国家级重点实验室，陕西　西安　710054
^3.西安测绘研究所，陕西　西安　710054

收稿日期:2025-04-29 修回日期:2025-10-15 出版日期:2025-11-14 发布日期:2025-11-14
通讯作者: 李姗姗 E-mail:txl101088@163.com;zzy_lili@sina.com
作者简介:谭勖立（1996—），男，博士生，研究方向为卫星重力测量。E-mail：txl101088@163.com
基金资助:
国家重点研发计划(2024YFC3212200)

Construction and analysis of the static gravity field model based on ChiGaM satellite

Xuli TAN¹(), Shanshan LI¹(), Zhiyong HUANG², Zongpeng PAN²^,³, Diao FAN¹, Hongfa WAN¹, Xianyong PEI¹, Zhenbang XU¹

^1.School of Geospatial Information, University of Information and Engineering, Zhengzhou 450001, China
^2.National Key Laboratory of Intelligent Spatial Information, Xi'an 710054, China
^3.Xi'an Research Institute of Surveying and Mapping, Xi'an 710054, China

Received:2025-04-29 Revised:2025-10-15 Online:2025-11-14 Published:2025-11-14
Contact: Shanshan LI E-mail:txl101088@163.com;zzy_lili@sina.com
About author:TAN Xuli (1996—), male, PhD candidate, majors in satellite gravimetry. E-mail: txl101088@163.com
Supported by:
The National Key Research and Development Program of China(2024YFC3212200)

摘要/Abstract

摘要：

中国重力测量计划ChiGaM（Chinese gravimetry augment and mass change exploring mission）的成功实施和持续运行，为实现独立自主恢复高精度地球重力场中长波信号提供了可能。本文研究了适用于ChiGaM卫星的高精度静态重力场模型构建方法，相较于传统动力学法反演过程：①估计了分段常加速度参数，选定了适用于ChiGaM卫星的参数先验方差；②采用PPS（pure predetermine strategy）策略估计KBR（K-band ranging）经验参数并考虑至3-CPR（cycle per revolution）项；③引入了抗差估计和经验剔除法，提高了模型反演精度。处理了卫星2022年3月至2024年5月间数据，构建了150阶静态重力场模型。为提高精度评估结果的可信度，引入RTM（residual terrain model）技术与超高阶重力场模型对地面、海洋重力数据不同频段信号进行分离。通过与频段信号分离后的地面和海洋重力数据对比，以及与GRACE（gravity recovery and climate experiment）卫星静态重力场模型横向对比，评估了所构建静态重力场模型精度。结果表明，本文方法可实现基于ChiGaM卫星的高精度静态重力场模型构建，同时验证了该卫星获取地球重力场中长波信号的能力。

关键词: 卫星重力测量, 静态重力场模型, ChiGaM卫星, 动力学法, RTM技术

Abstract:

The successful implementation and continuous operation of China's ChiGaM (Chinese gravimetry augment and mass change exploring mission) have made it possible to independently and autonomously recover medium-to-long wavelength signals of the Earth's gravity field with high accuracy. This paper investigates a method for recovering a high-precision static gravity field model based on ChiGaM satellite data. Compared with traditional dynamic approach, the proposed method includes following improvements: ① Estimation of piecewise constant acceleration parameters and selection of appropriate priori variance of these parameters for ChiGaM satellite. ② Application of the pure predetermine strategy (PPS) to estimate K-band ranging (KBR) empirical parameters up to the 3-cycle per revolution (3-CPR) terms. ③ Incorporation of robust estimation and empirical data elimination techniques to enhance the inversion accuracy. Using data collected from March 2022 to May 2024, a 150-degree static gravity field model was developed. To improve the reliability of accuracy evaluation, residual terrain model (RTM) technology and ultra-high-degree gravity field models were employed to separate signals, in different frequency bands, from terrestrial and marine gravity data. The accuracy of the constructed static gravity field model was assessed through comparisons with the frequency-separated terrestrial and marine gravity data, as well as through cross-comparison with the GRACE (gravity recovery and climate experiment) static gravity field models. The results demonstrate that the proposed method enables the construction of a high-precision static gravity field model using ChiGaM satellite data, further validating the satellite's capability to capture medium-to-long wavelength signals of the Earth's gravity field.

Key words: satellite gravimetry, static gravity field model, ChiGaM satellite, dynamic approach, RTM technique

中图分类号:

P223

谭勖立, 李姗姗, 黄志勇, 潘宗鹏, 范雕, 万宏发, 裴宪勇, 徐振邦. ChiGaM卫星静态重力场模型构建与分析[J]. 测绘学报, 2025, 54(10): 1798-1811.

Xuli TAN, Shanshan LI, Zhiyong HUANG, Zongpeng PAN, Diao FAN, Hongfa WAN, Xianyong PEI, Zhenbang XU. Construction and analysis of the static gravity field model based on ChiGaM satellite[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(10): 1798-1811.

图/表 15

表1

图1

图2

图3

图4

表2

表3

表4

表5

图5

表6

图6

表7

图7

表8

参考文献 45

[1]	许厚泽, 陆洋, 钟敏, 等. 卫星重力测量及其在地球物理环境变化监测中的应用[J]. 中国科学：地球科学, 2012, 42(6): 843-853.
	XU Houze, LU Yang, ZHONG Min, et al. Satellite gravimetry and its application in monitoring the change of geophysical environment[J]. Scientia Sinica (Terrae), 2012, 42(6): 843-853.
[2]	宁津生, 王正涛, 超能芳. 国际新一代卫星重力探测计划研究现状与进展[J]. 武汉大学学报(信息科学版), 2016, 41(1): 1-8.
	NING Jinsheng, WANG Zhengtao, CHAO Nengfang. Research status and progress in international next-generation satellite gravity measurement missions[J]. Geomatics and Information Science of Wuhan University, 2016, 41(1): 1-8.
[3]	宁津生. 卫星重力探测技术与地球重力场研究[J]. 大地测量与地球动力学, 2002, 22(1): 1-5.
	NING Jinsheng. The satellite gravity surveying technology and research of Earth's gravity field[J]. Crustal Deformation and Earthquake, 2002, 22(1): 1-5.
[4]	宁津生. 跟踪世界发展动态　致力地球重力场研究[J]. 武汉大学学报(信息科学版), 2001, 26(6): 471-474, 486.
	NING Jinsheng. Following the developments of the world, devoting to the study on the Earth gravity field[J]. Editoral Board of Geomatics and Information Science of Wuhan University, 2001, 26(6): 471-474, 486.
[5]	郑伟, 许厚泽, 钟敏, 等. 地球重力场模型研究进展和现状[J]. 大地测量与地球动力学, 2010, 30(4): 83-91.
	ZHENG Wei, XU Houze, ZHONG Min, et al. Progress and present status of research on Earth's gravitational field models[J]. Journal of Geodesy and Geodynamics, 2010, 30(4): 83-91.
[6]	冯进凯, 王庆宾, 黄佳喜, 等. 多个超高阶重力场模型精度分析[J]. 测绘科学技术学报, 2017, 34(4): 358-363.
	FENG Jinkai, WANG Qingbin, HUANG Jiaxi, et al. The accuracy analysis of multiple ultra-high-degree gravity field models[J]. Journal of Geomatics Science and Technology, 2017, 34(4): 358-363.
[7]	罗志才, 钟波, 周浩, 等. 利用卫星重力测量确定地球重力场模型的进展[J]. 武汉大学学报(信息科学版), 2022, 47(10): 1713-1727.
	LUO Zhicai, ZHONG Bo, ZHOU Hao, et al. Progress in determining the Earth's gravity field model by satellite gravimetry[J]. Geomatics and Information Science of Wuhan University, 2022, 47(10): 1713-1727.
[8]	ZHOU Hao, LUO Zhicai, ZHOU Zebing, et al. HUST-Grace2016s: a new GRACE static gravity field model derived from a modified dynamic approach over a 13-year observation period[J]. Advances in Space Research, 2017, 60(3): 597-611.
[9]	CHEN Qiujie, SHEN Yunzhong, FRANCIS O, et al. Tongji-Grace02s and Tongji-Grace02k: high-precision static GRACE-only global earth's gravity field models derived by refined data processing strategies[J]. Journal of Geophysical Research: Solid Earth, 2018, 123(7): 6111-6137.
[10]	KVAS A, BROCKMANN J M, KRAUSS S, et al. GOCO06s-a satellite-only global gravity field model[J]. Earth System Science Data, 2021, 13(1): 99-118.
[11]	SHAKO R, FÖRSTE C, ABRIKOSOV O, et al. EIGEN-6C: a high-resolution global gravity combination model including GOCE data[M]//Observation of the System Earth from Space-CHAMP, GRACE, GOCE and future missions. Berlin: Springer Berlin Heidelberg, 2013: 155-161.
[12]	ZINGERLE P, PAIL R, GRUBER T, et al. The combined global gravity field model XGM2019e[J]. Journal of Geodesy, 2020, 94(7): 66.
[13]	肖云, 杨元喜, 潘宗鹏, 等. 中国卫星跟踪卫星重力测量系统性能与应用[J]. 科学通报, 2023, 68(20): 2655-2664.
	XIAO Yun, YANG Yuanxi, PAN Zongpeng, et al. Performance and application of the Chinese satellite-to-satellite tracking gravimetry system[J]. Chinese Science Bulletin, 2023, 68(20): 2655-2664.
[14]	XIAO Yun, YANG Yuanxi, PAN Zongpeng, et al. Chinese gravimetry augment and mass change exploring mission status and future[J]. Journal of Geodesy and Geoinformation Science, 2023, 6(3).
[15]	杨元喜, 王建荣, 楼良盛, 等. 航天测绘发展现状与展望[J]. 中国空间科学技术, 2022, 42(3): 1-9.
	YANG Yuanxi, WANG Jianrong, LOU Liangsheng, et al. Development status and prospect of satellite-based surveying[J]. Chinese Space Science and Technology, 2022, 42(3): 1-9.
[16]	ZHOU Hao, LUO Zhicai, ZHOU Zebing, et al. Impact of different kinematic empirical parameters processing strategies on temporal gravity field model determination[J]. Journal of Geophysical Research: Solid Earth, 2018, 123(11): 10, 252-10, 276.
[17]	游为. 应用低轨卫星数据反演地球重力场模型的理论和方法[D]. 成都: 西南交通大学, 2011.
	YOU Wei. Theory and methodology of Earth's gravitational field model recovery by Leo data[D]. Chengdu: Southwest Jiaotong University, 2011.
[18]	DARBEHESHTI N, LASSER M, MEYER U, et al. AIUB-GRACE gravity field solutions for G3P: processing strategies and instrument parameterization[J]. Earth System Science Data, 2024, 16(3): 1589-1599.
[19]	WÖSKE F, KATO T, RIEVERS B, et al. GRACE accelerometer calibration by high precision non-gravitational force modeling[J]. Advances in Space Research, 2019, 63(3): 1318-1335.
[20]	ZHANG Jiahui, YOU Wei, YU Biao, et al. GRACE-FO accelerometer performance analysis and calibration[J]. GPS Solutions, 2023, 27(4): 158.
[21]	BEUTLER G, JÄGGI A, MERVART L, et al. The celestial mechanics approach: theoretical foundations[J]. Journal of Geodesy, 2010, 84(10): 605-624.
[22]	BEUTLER G, JÄGGI A, MERVART L, et al. The celestial mechanics approach: application to data of the GRACE mission[J]. Journal of Geodesy, 2010, 84(11): 661-681.
[23]	MEYER U, JÄGGI A, JEAN Y, et al. AIUB-RL02: an improved time-series of monthly gravity fields from GRACE data[J]. Geophysical Journal International, 2016, 205(2): 1196-1207.
[24]	NIE Yufeng, SHEN Yunzhong, PAIL R, et al. Revisiting force model error modeling in GRACE gravity field recovery[J]. Surveys in Geophysics, 2022, 43(4): 1169-1199.
[25]	ZHONG Bo, LI Qiong, CHEN Jianli, et al. Improved estimation of regional surface mass variations from GRACE intersatellite geopotential differences using a priori constraints[J]. Remote Sensing, 2020, 12(16): 2553.
[26]	LUTHCKE S B, ROWLANDS D D, LEMOINE F G, et al. Monthly spherical harmonic gravity field solutions determined from GRACE inter-satellite range-rate data alone[J]. Geophysical Research Letters, 2006, 33(2): 356-360.
[27]	SHEN Zhanglin, CHEN Qiujie, SHEN Yunzhong. An improved acceleration approach by utilizing K-band range rate observations[J]. Remote Sensing, 2023, 15(21): 5260.
[28]	YANG Y, CHENG M K, SHUM C K, et al. Robust estimation of systematic errors of satellite laser range[J]. Journal of Geodesy, 1999, 73(7): 345-349.
[29]	王培杰, 陈小斌, 韩鹏, 等. 基于稳健估计、数据筛选和Rhoplus约束的大地电磁数据处理方法[J]. 地球物理学报, 2024, 67(11): 4325-4342.
	WANG Peijie, CHEN Xiaobin, HAN Peng, et al. Strong interference magnetotelluric data processing method based on robust estimation, data screening and Rhoplus constraint[J]. Chinese Journal of Geophysics, 2024, 67(11): 4325-4342.
[30]	孙悦, 薛树强, 韩保民, 等. 邻近海底基准站坐标时序联合处理模型[J]. 测绘学报, 2023, 52(11): 1835-1843. DOI: . doi: 10.11947/j.AGCS.2023.20220203
	SUN Yue, XUE Shuqiang, HAN Baomin, et al. Multi-station joint processing model for seafloor geodetic coordinate time series[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52(11): 1835-1843. DOI: . doi: 10.11947/j.AGCS.2023.20220203
[31]	LYARD F H, ALLAIN D J, CANCET M, et al. FES2014 global ocean tide atlas: design and performance[J]. Ocean Science, 2021, 17(3): 615-649.
[32]	PETIT G, LUZUM B. IERS conventions (2010)[J]. IERS Technical Note, 2010, 36. DOI: . doi: http://dx.doi.org/
[33]	FOLKNER W, WILLIAMS J, BOGGS D, et al. The planetary and lunar ephemerides DE430 and DE431[R]. [S.l.]: Interplanetary network progress report, 2014, 196(1): 42-196.
[34]	DESAI S D. Observing the pole tide with satellite altimetry[J]. Journal of Geophysical Research: Oceans, 2002, 107(C11): 7-1-7-13.
[35]	DOBSLAW H, BERGMANN-WOLF I, DILL R, et al. A new high-resolution model of non-tidal atmosphere and ocean mass variability for de-aliasing of satellite gravity observations: AOD1B RL06Free[J]. Geophysical Journal International, 2017, 211(1): 263-269.
[36]	HIRT C, GRUBER T, FEATHERSTONE W E. Evaluation of the first GOCE static gravity field models using terrestrial gravity, vertical deflections and EGM2008 quasigeoid heights[J]. Journal of Geodesy, 2011, 85(10): 723-740.
[37]	HIRT C, YANG Meng, KUHN M, et al. SRTM2gravity: an ultrahigh resolution global model of gravimetric terrain corrections[J]. Geophysical Research Letters, 2019, 46(9): 4618-4627.
[38]	KVAS A, BEHZADPOUR S, ELLMER M, et al. ITSG-Grace2018: overview and evaluation of a new GRACE-only gravity field time series[J]. Journal of Geophysical Research: Solid Earth, 2019, 124(8): 9332-9344.
[39]	AKYILMAZ O, USTUN A, AYDIN C, et al. ITU_GRACE16: the global gravity field model including GRACE data up to degree and order 180 of ITU and other collaborating institutions[EB/OL]. [2025-01-25]. DOI: http://doi.org/10.5880/icgem.2016.006.
[40]	MAYER-GURR T, EICKER A, ILK K H. ITG-Grace02s: a GRACE gravity field derived from range measurements of short arcs[C]//Proceedings of the 1st International Symposium of the International Gravity Field Service. Ankara: Command of Mapp, 2007.
[41]	RIES J, BETTADPUR R, EANES Z, et al. The development and evaluation of the global gravity Model GGM05[R]. Texas: Center for Space Research, 2016. DOI: . doi: http://dx.doi.org/10.26153/tsw/1461
[42]	TAPLEY B, RIES J, BETTADPUR S, et al. GGM02-an improved Earth gravity field model from GRACE[J]. Journal of Geodesy, 2005, 79(8): 467-478.
[43]	KVAS A, BROCKMANN J M, KRAUSS S, et al. GOCO06s—a satellite-only global gravity field model[J]. Earth System Science Data, 2021, 13(1): 99-118.
[44]	ANDERSEN O B, KNUDSEN P. The DTU17 global marine gravity field: first validation results[M]//Fiducial Reference Measurements for Altimetry. Cham: Springer International Publishing, 2019: 83-87.
[45]	GUO Jinyun, WEI Xuyang, LI Zhen, et al. SDUST2023GRA_MSS: the new global marine gravity anomaly model determined from mean sea surface model[J]. Scientific Data, 2025, 12(1): 108.

方案	σ₁值	σ₂值	σ₁₂值
方案1	3×10^-8	3×10^-8	不考虑
方案2	3×10^-8	3×10^-8	3×10^-10
方案3	3×10^-9	3×10^-9	不考虑
方案4	3×10^-9	3×10^-9	3×10^-10
方案5	3×10^-9	3×10^-9	3×10^-11
方案6	3×10^-10	3×10^-10	不考虑
方案7	3×10^-10	3×10^-10	3×10^-11
方案8	3×10^-11	3×10^-11	不考虑
方案9	3×10^-11	3×10^-11	3×10^-11

背景场	模型	描述
地球重力场	EIGEN-6C4^[11]	截断至360阶
海洋潮汐	FES2014b^[31]	截断至180阶，包含34个主潮汐和327个次潮汐分量，基于导纳理论内插次潮汐分量
固体潮汐	IERS convention 2010^[32]	考虑至4阶项，同时顾及频率相关项和频率无关项，潮汐系统采用tide free
三体引力摄动	质量点模型	采用DE430星历^[33]，考虑太阳系主要星体，考虑J2项影响
固体极潮	IERS convention 2010	仅考虑C21和S21项，平均极移采用线性模型
海洋极潮	Desai模型^[34]	截断至180阶，平均极移采用线性模型
大气潮汐	AOD1B RL06^[35]	截断至180阶，包含12个主潮汐分量
海洋大气非潮汐变化	AOD1B RL06	截断至180阶，节点之间采用线性内插

参数名称	属性	设定
球谐系数	全局参数	2~150阶，共22 797个参数
卫星初始运动状态改正参数	局部参数	每颗卫星每弧段（3 h）估计1组，每组6个参数
加速度计标校参数	局部参数	偏移参数每颗卫星每弧段（3 h）估计1组，每组3个参数；尺度因子参数每颗卫星每天估计1组，包含对角线和非对角线元素，每组9个参数
分段常加速度	局部参数	每颗卫星每15 min估计1组，每组3个参数，添加约束
KBR经验参数	局部参数	线性项每0.75 h估计1组，每组2个参数；周期项每1.5 h估计1组，周期为1.5 h，每组12个参数。单独估计

名称	采样率/Hz	描述
ROE1B	1	卫星简化动力学定轨数据，包含卫星的位置和速度及其方差
KBR1B	5	星间微波测距数据，包含星间距离（有偏）、星间距离变率和星间距离加速度
ACC1B	1	卫星加速度计数据，包含卫星非保守力加速度在卫星科学坐标系三轴方向上的分量
SCA1B	1	卫星姿态数据，包含从惯性系到卫星科学坐标系的转换四参数

模型	阶次	使用数据	反演方法	发布机构
IEU-CGS-Static2024	150阶（静态）	ChiGaM卫星2022-03—2024-05	动力学法	信息工程大学
GGM02S	160阶（静态）	GRACE卫星2002-04—2003-12	动力学法	CSR
GGM05S	180阶（静态）	GRACE卫星2003-03—2013-05	动力学法	CSR
HUST-Grace2016s	160阶（静态）	GRACE卫星2003-01—2015-04	改进动力学法	华中科技大学
ITG-Grace02s	160阶（静态）	GRACE卫星2002-02—2005-12	短弧法	波恩大学
ITSG-Grace2018s	200阶（静态）+120阶（时变）	GRACE卫星2002-04—2016-08	动力学法	格拉茨技术大学
ITU_GRACE16	180阶（静态）	GRACE卫星2009-04—2013-10	能量法	俄亥俄州立大学（主导）联合多机构
Tongji-Grace02s	180阶（静态）+50阶（时变）	GRACE卫星2003-01—2016-07	改进短弧法	同济大学

ChiGaM卫星静态重力场模型构建与分析

Construction and analysis of the static gravity field model based on ChiGaM satellite

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

图/表 15

参考文献 45

相关文章 3

编辑推荐

Metrics

本文评价

重力场模型	60阶次	96阶次	120阶次	150阶次
GGM02S	0.55	1.90	8.31	56.09
GGM05S	0.12	0.42	1.38	7.71
HUST-Grace2016s	0.07	0.30	1.25	6.80
ITG-Grace02s	0.17	0.52	1.96	9.20
ITSG-Grace2018s	0.11	0.19	0.60	1.19
ITU_GRACE16	0.15	0.99	8.54	32.35
Tongji-Grace02s	0.07	0.19	0.71	2.72
IEU-CGS-Static2024	0.15	0.58	2.00	11.37

重力场模型	西部山区	东部平原	总体
GGM02S	6.06	7.13	6.76
GGM05S	2.38	1.91	2.10
HUST-Grace2016s	2.17	1.60	1.83
ITG-Grace02s	2.45	1.70	2.01
ITSG-Grace2018s	2.02	1.12	1.51
ITU_GRACE16	10.03	11.41	10.92
Tongji-Grace02s	2.08	1.34	1.65
IEU-CGS-Static2024	2.20	1.94	2.04

重力场模型	海洋重力异常模型的差值RMS
重力场模型	SIO_V32.1	DTU17	SDUST2023 GRA_MSS
GGM02S	10.57	10.57	10.56
GGM05S	1.56	1.58	1.48
HUST-Grace2016s	1.44	1.46	1.35
ITG-Grace02s	1.90	1.93	1.84
ITSG-Grace2018s	0.80	0.85	0.64
ITU_GRACE16	5.23	5.24	5.21
Tongji-Grace02s	0.90	0.95	0.76
IEU-CGS-Static2024	2.29	2.30	2.23

[1]	祝竺, 赵艳彬, 廖鹤, 涂海波, 张国万, 魏小刚. 星载原子干涉技术用于地球重力场测量及其精度评估[J]. 测绘学报, 2017, 46(9): 1088-1097.
[2]	沈云中. 动力学法的卫星重力反演算法特点与改进设想[J]. 测绘学报, 2017, 46(10): 1308-1315.
[3]	陈秋杰, 沈云中, 张兴福, 陈武, 许厚泽. 基于GRACE卫星数据的高精度全球静态重力场模型[J]. 测绘学报, 2016, 45(4): 396-403.